Time-frequency domain reflectometry apparatus and method

ABSTRACT

An apparatus and method for high-resolution reflectometry that operates simultaneously in both the time and frequency domains, utilizing time-frequency signal analysis and a chirp signal multiplied by a Gaussian time envelope. The Gaussian envelope provides time localization, while the chirp allows one to excite the system under test with a swept sinewave covering a frequency band of interest. High resolution in detection of the reflected signal is provided by a time-frequency cross correlation function. The high-accuracy localization of faults in a wire/cable can be achieved by measurement of time delay offset obtained from the frequency offset of the reflected signal. The apparatus enables one to execute an automated diagnostic procedure of a wire/cable under test by control of peripheral devices.

TECHNICAL FIELD OF THE INVENTION

The present invention is a new apparatus and methodology ininstrumentation and measurement for detection and localization of thefaults in a wire or cable of an electric or electronic system where highlevel of reliability is required. In particular, the invented apparatusis capable of detection and localization of faults in high resolutionbased on the time-frequency domain reflectometry methodology that allowsone to consider time and frequency simultaneously while the conventionalapparatus and methods rely on either time or frequency only. Therefore,the invented apparatus and method achieve higher accuracy in detectionand localization of faults in variety types of cable and wire.

THE STATE OF THE ART

The importance of electrical wiring and associated faults has beenhighlighted by the investigation of several aircraft crashes. A tinyfault on a wire might cause arcing, which may result in serious damagesto the overall system. This problem is not limited to commercialaircraft only systems where complicated wiring is involved and highersafely is required, like military aircraft, space shuttle, nuclear powerplants and very tall buildings, etc., might face wiring problems. Thusdetection of faults with high resolution is required for diagnosis andmaintenance of wiring systems.

The detection and localization of faults in electric cable or wire arethe important technical task to the instrumentation and measurementengineering, which is an application of cable tester and impedance ornetwork analyzer. Also the cable and wire manufacturers demandhigh-resolution detection and localization of faults for their productquality assurance.

The reflectometry is a fundamental basis for detection and location ofcables sent for diagnosis of a wiring system. The principles of thereflectometry is to compare the transmitted reference signal and thereflected signal from the faults or discontinuity of a conductor for ordetection and localization.

The contemporary state-of-art for wiring/cable fault detection can becategorized by time domain analysis and frequency domain analysis. Intime domain analysis, time domain reflectometry (TDR) is used, whereasin frequency domain analysis, frequency domain reflectometry (FDR) andstanding wave reflectometry (SWR) are utilized The application of thereflectometry is extended to optical known as optical frequency domainreflectometry (OFDR). Each methodology is based on the appropriateanalysis of the reference signal and reflected signal either in the timeor frequency domain only. Some TDR based commercial electronic devicesto test the health of wiring are available in the market. The frequencydomain reflectometry (FDR) and standing wave reflectometry (SWR) employanalysis of the reference signal and reflected signal in the frequencydomain, and the SWR-based systems are under development.

However, technical problems with these methodologies are the fact thattheir resolution and accuracy performance for detection and localizationare limited, because both time domain reflectometry and frequency domainreflectometry rely on the analysis of the reflected signals in only onedomain, either time or frequency.

In TDR a step pulse is applied to the wire/cable under test which isthen reflected by any faults present. The time it takes for thereflected signal to make a round trip can then be converted to distancefrom the knowledge of the velocity of propagation. A drawback of thismethod is that its resolution is limited by rise time of the pulse wave.Since the energy of the impulse is spread over a broad frequency range,TDR is usually not suitable for investigating the RF properties of acable, which is important, for example, when dealing with wires/cablesused for communication purposes.

On the other hand, FDR often uses a swept frequency signal which allowsone to place the energy of the reference or probing signal in the RFband of interest. The FDR detects and locates faults as well ascharacteristic impedance of an electric conductor by directly measuringthe phase differences between an input wave and the reflected wave ofthe conductor, wherein a sinusoidal wave serves as the reference signs.When a fault is existent in the conductor, a resonance between the twosignals is produced. The FDR, being a method for analyzing signals infrequency domain alone, is limited in its resolution by sweep bandwidth.Furthermore, it has a drawback that its accuracy in distance estimationof faults is lowered in the presence of noise as in case of the TDP.

DISCLOSURE OF THE INVENTION

The present invention, conceived in view of the foregoing, aims toprovide time-frequency domain reflectometry apparatus capable ofarchitecting an input signal in time-frequency domain fitting tofrequency characteristics of a conductor under test. By investigatingthe reflected and reference signals in time domain as well as infrequency domain simultaneously using time-frequency domainreflectometry using the apparatus.

The new invention of methodology that we introduce is a jointtime-frequency domain reflectometry (TFDR) technique can becharacterized by its capability which captures many of the advantages ofTDR and FDR mentioned previously. The reference signal is a chirpsignal, which allows one to apply the RF power in the band of interest.To provide time localization, the chirp signal is multiplied by aGaussian envelope in the time domain. The design of reference signal intime and frequency domain is the generalization of the contemporaryreflectometry in time or frequency domain only time-frequency domainreflectometry can be characterized by time and frequency localization asa mixture of time domain reflectometry and frequency domainreflectometry. For example, under the conditions with no frequency sweepand the duration of the Gaussian envelope is very large, the referencesignal of the time-frequency domain reflectometry takes on a pulse-likecharacter reminiscent of the reference signal of TDR. Similarly, for avery small duration of the Gaussian envelope, the reference signal ofthe time-frequency domain reflectometry corresponds to the sweptsinusoidal reference signal of FDR. Therefore, the time-frequency domainreflectometry scheme provides flexible application depending on thephysical characteristics of the wire or cable under test. Note that thereference signals in TDR or FDR is constrained in time and frequencydomain, respectively.

For the detection and localization, the time-frequency distributions ofthe reference signal and the reflected signals are calculated. Thenthese two time-frequency distributions are cross-correlated in thetime-frequency domain. The peak in the time-frequency cross correlationfunction allows one to estimate an accurate round-trip propagation timeand, hence, distance, as in classical TDR. However, for ahigher-accuracy localization of the fault, the measured arrival time iscompensated by the frequency offset of the reflected signal which can beconverted into time information. This is an unique feature of thetime-frequency domain reflectometry for the high-resolution detectionand localization where the time and frequency information is treatedsimultaneously. Yet, the experiment is carried in an RF band of interestwhich is relevant for the particular wire/cable under test, as in FDR.The detailed description of the algorithm will be presented in nextsection.

Another object of the present invention is to provide time-frequencydomain reflectometry apparatus having a wide spectrum of applications ingeographic/resource surveys, material surface tests, radar/sonarpurposes, communication network wirings, optical cable diagnoses, remoteexplorations, fluid pipe leakage detections, water gauges, etc. inaddition to the conventional application in detecting and locating offaults in a conductor, with a new access method in reflectometry forprocessing signals that allows architecting an input signal andprocessing thereof in a time-frequency domain.

In order to achieve the above objects, a time-frequency domainreflectometry apparatus for detection and localization is composed offollowing components: a personal computer (PC) capable of performingmain control program of a predetermined time-frequency domainreflectometry, including a device control program that controls controlexternal instrumentation devices for the generation of the referencesignal and acquisition of the reflected signs. The system consists of acirculator, the waveform generator and the data acquisition equipmentwhich is connected to a computer with GPIB cable for automatic controlof the instruments. The computer controls the waveform generator toproduce the Gaussian envelope chirp signal which propagates into thetarget cable via the circulator. This reference signal is reflected atthe fault location and back to the circulator. The circular redirectsthe reflected signal to the data acquisition equipment. The computercontrols and synchronizes the waveform generator and data acquisitionequipment, calculates the time-frequency distribution of the referencesignal and reflected signals, and executes the time-frequency crosscorrelation algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing control process in a time-frequencydomain reflectometry apparatus in accordance with the present invention.

FIGS. 2( a)-2(c) show a time-frequency distribution of a chirp signalwith Gaussian envelope which is the reference signal of thetime-frequency domain reflectometry apparatus for explanation of thepresent invention.

FIG. 3 is a flow chart shows process of algorithm in a time-frequencydomain reflectometry method in accordance with the present invention.

FIG. 4 shows an example of screen snapshot for GUI program control inaccordance with the present invention.

FIG. 5 depicts time-frequency domain distributions of W_(s)(t,ω)(reference signal), W_(s)(t−t_(d),ω)(transmitted signal), andW_(u(x))(t,ω) (reflected signal) in accordance with the presentinvention.

FIG. 6 depicts an experimental simulation setup for a faulty coaxialcable testing simulation in accordance with an embodiment of the presentinvention.

FIG. 7 shows time (a) and frequency (b) marginals of the time-frequencydistributions of the individual signals in the experiment described inFIG. 6. (Note that the individual distributions are normalized forillustration. Time centers are shifted to that of the reference signal.)

FIG. 8 illustrates frequency response of the coaxial cable for normaland faulty state in amplitude in (a) and phase (b) characteristics ofthe conductor under experiment of FIG. 6.

FIG. 9 illustrates the reflected waveform of the faulty coaxial cable intime domain at node 1 with fault in (a) and transmitted waveform in timedomain without fault at node 2 in the experiment of FIG. 6.

FIG. 10 illustrates the time-frequency cross correlation functionsbetween the input reference signal and the reflected waveform of thefaulty coaxial at node 1 with fault in (a) and transmitted waveformwithout fault at node 2 provided in FIG. 9.

BRIEF EXPLANATION OF THE MAIN FIGURES IN THE DRAWINGS

100: PC

110: Device Control Program

120: Time-Frequency Domain Reflectometry Detection and EstimationAlgorithm

130: Processor Control Program

200: Digital Signal Processing (DSP)

300: Reference Waveform Generator

400: Data Acquisition Instrument (DAI)

500: GUI Program

600: Electric Cable/Wire Under Test

700: Circulator

BEST MODE FOR CARRYING OUT THE INVENTION

Now, construction of the present invention is explained below in moredetail by describing the implementation of the invention with theaccompanying drawings.

FIG. 1 is a block diagram showing control process in a time-frequencydomain reflectometry apparatus in accordance with the present invention.

As shown above, Numeral 100, which represents a personal computer (PC),is a device where the main program of a time-frequency domainreflectometry apparatus in accordance with the present invention isexecuted.

Numeral 200, representing a DSP, computes time-frequency distributionfunctions.

Numeral 300, representing an AWC; generates input reference signals fora wire/conductor under test.

Numeral 400, representing a DAI, acquires reflected signal from awire/conductor under test as well as input signal generated by an AWGvia a circulator, and stores the same.

For the execution of the detection and localization, the above AWG 300generates input reference signal-chirp signals. A chirp signal is asignal, of which the frequency changes in a linear manner with elapse oftime. The chirp signal adopted here is one, of which the frequency riseslinearly with time.

In this invention, the chirp signal is multiplied by the Gaussianenvelope so that a localization in time-frequency domain could beaccomplished (cf. FIG. 2). An explicit expression of the referencesignal to be generated is as follows:s(t)=(α/π)^(1/4) e ^(−α(t−t) ⁰ ⁾ ² ^(/2+jβ(t−t) ⁰ ⁾ ² ^(/2+jω) ⁰ ^((t−t)⁰ ⁾where t and t₀ stand for time and initial time, respectively, αstandsfor Gaussian constant, β stands for frequency increase rate, and ω₀stands for angular velocity.

Parameter value for signal generation is applied through the AWG 300 andGPIB programming of the PC 100, while the operations of reference signalgeneration are controlled by the PC 100. The generated input referencesignal thus is applied to the wire/cable under test, and when itconfronts a fault, the other parts of the signal are transmittedfurther. An oscilloscope captures the reflected wave as well as thetransmitted wave from each channel, and then displays them on a screen,which operation is performed also by GPIB programming Also the acquireddata is stored as a numerical file which is transferred to the PC 100for the execution of the detection and localization algorithm Theparameter values of the input reference signal can be modified by the PC100 in accordance with the attenuation characteristics of a wire/cableunder test even during a triggering operation.

The process control program 130 receives the two files inputted from thePC through a GPIB cable and transmits the same to the DSP 200. The DSP200 compares signal [S(t)] information with data fetched from theoscilloscope to detect faults in the wire/cable under test, computes tolocalize the faults using a time-frequency domain reflectometrydetection and estimation algorithm 120 of the DSP program. An easycontrol of the PC 100 as well as of external devices, such as monitor,key board, buttons, etc. could be enabled using the GUI program 500.With the GUI program 500, parameter values for different conductors 600,input wave, output wave, etc. can be displayed on a monitor as shown in{circle around (1)} of FIG. 4, architecture of a desired chirp signalcan be substituted by input of parameters as in {circle around (2)} ofFIG. 4, the wave forms of input signal and output signal can berepresented visually as in {circle around (3)} and {circle around (4)}of FIG. 4, visual analysis as well as representation of a resultingvalue in numerals are also enabled as in {circle around (5)} of FIG. 4,and control of entire external devices through simple keyboard inputsand button clicks are enabled.

FIG. 3 is a flow chart showing control process in a time-frequencydomain reflectometry method in accordance with the present invention. Asshown in the drawing, a time-frequency domain reflectometry method asper the present invention, i.e. a method for detecting and locatingfaults in an electric wire/cable under test in accordance with thepresent invention comprises the step: of inputting (S10) values forphysical and electric characteristics of a wire/cable under test 600under test using GUI, after the wire/cable under test has been connectedto a system via a cable and then the system has been initialized; ofselecting a frequency domain (S11) suitable to the estimatedcharacteristics of the wire/cable under test in a frequency domain,after size and phase of a reflected wave in the frequency domain hasbeen estimated on the basis of an inputted value of the wire/cable undertest; of selecting a minimal time distribution (S12) that satisfies theuncertainty principle between the selected frequency and the time in theabove selected frequency domain; of architecting an optimal inputreference signal (S13) through multiplication of a Gaussian envelope ofthe selected time distribution by a chirp signal occupying the selectedfrequency domain; of generating the reference signal (S14) by an AWG 300for a wire/cable under test 600 to be tested physically, after the abovearchitected wave form has been transmitted to the AWG 300 via a GPIB; ofstoring wave form of the reflected wave (S15) passed through thewire/cable under test 600 from the DAI 400 and transmitting the waveform to the inner program in form of a file simultaneously with theabove step of generating reference signal; of computing a time-frequencydistribution function (S16) from the received wave form signal by theDSP 200 for a rapid calculation; of detecting faults (S17) in thewire/cable under test 600 considering the inputted electromagneticcharacteristics of the wire/cable under test after time-frequency crosscorrelation functions have been computed from the input signal and thetime-frequency distribution functions of the reflected wave; oflocalizing the reflected wave (S18) using the time-frequency correlationfunction, if any fault is diagnosed; and of estimating the correctlocation of faults in the wire/cable under test (S19) after localizedtime delays, frequency displacements of the reflected wave have beencomputed from marginal of the time-frequency distribution function forthe above localized signal, and then the signal distortions have beencompensated by time-frequency increase rate of the architected signal.

The time-frequency domain reflectometry as above is described in moredetail below. The present invention presents an improved input signaland a processing method to realize a higher level of accuracy incomparison to the conventional art. In other words, an input signal asarchitected in the present invention is a time localized chirp signalhaving the following characteristics: This input signal is designed asstanding wave having a size of Gaussian distribution in time domain aswell as in frequency domain so that it could be interpreted in both timedomain and frequency domain, and having a limited bandwidth with itsfrequency changing linearly. Since this signal is shaped to correspondto a Gaussian distribution, it shows a higher accuracy in respect todispersiveness, pulse spread, noise, and distortion compared to a timedomain reflectometry (TDR), which uses pulse wave.

Further, the TDR interprets input wave and output wave in time domainalone for detecting and locating faults in a wire/cable under test whilethe frequency domain reflectometry (FDR) and the standing wavereflectometry (SWR) interprets the same only in frequency domain. Incontrast thereto, an input signal as per the present invention isarchitected to be interpreted in both time domain and in frequencydomain, so that an accuracy higher than that obtained through aninterpretation in either one of time domain or frequency domain can beachieved.

Moreover, the present invention provides a time-frequency domainreflectometry (TFDR) for interpretation of an input signal in both timedomain and frequency domain. For interpretation in both time domain andfrequency domain of an input signal as architected in the presetinvention as well as the reflected signal, the present invention usesWigner distinction, which is a function representing distribution of asignal in time domain and frequency domain. The input signal architectedin the present invention can be formulated as follows:s(t)=(α/π)^(1/4) e ^(−α(t−t) ⁰ ⁾ ² ^(/2+jβ(t−t) ⁰ ⁾ ² ^(+jω) ⁰ ^((t−t) ⁰⁾  (1)where α denotes the width determination factor of Gaussian distribution,β denotes the frequency increase rate factor to time. A time center(t_(s)) and a time duration (T_(s)) of a signal on time axis can beobtained using Formula (1):t _(s) =∫t|s(t)|² dt=t ₀ T _(s) ²=∫(t−t _(s))² └s(t)┘² dt=½α  (2)

Further, a frequency center (ω₀) and a bandwidth (B_(s)) on frequencyaxis can be obtained from Fourier transform (Formula 3)) of the inputsignal as follows:

$\begin{matrix}{{S(\omega)} = {\sqrt{\frac{\sqrt{\alpha}}{\sqrt{\pi\left( {\alpha - {j\beta}} \right)}}}{\mathbb{e}}^{\frac{{({\omega - \omega_{0}})}^{2}}{2{({\alpha - {j\beta}})}}}}} & (3) \\{{\omega_{s} = {{\int{\omega{{S(\omega)}}^{2}{\mathbb{d}\omega}}} = \omega_{0}}}{B_{s}^{2} = {{\int{\left( {\omega - \omega_{0}} \right)^{2}{{S(\omega)}}^{2}{\mathbb{d}\omega}}} = \frac{\alpha^{2} + \beta^{2}}{2\;\alpha}}}} & (4)\end{matrix}$

In the same manner, a time center (t_(r)) and a time duration (T_(r)) ofreflected signal on time axis, a frequency center (ω_(r)) and abandwidth (B_(r)) of a reflected signal on frequency axis can beobtained using Formula (2) and Formula (4).

Accordingly, in order that an input signal is applied to an objectwire/cable under test, the input signal shall be designed to fit to thefrequency-dependent attenuation characteristics of the wire/cable undertest through selections of parameters α, β, and ω₀ of the signal. Aparameter determination process of a signal comprises the followingsteps of:

-   -   1. Obtaining (characteristics of a wire/cable under test by)        size and phase difference;    -   2. Selecting a maximal frequency in view of the size attenuation        in frequency domain;    -   3. Selecting a minimal frequency in view of frequency (band)        width of the AWG and of the waveform branching instrument from        difference in frequency with the maximal frequency;    -   4. Determining parameter α, after having selected a time domain        width larger than the reciprocal oft he above selected frequency        (band) width; and    -   5. Determining β by computing the frequency increase rate        between the lowest frequency and the highest frequency within        the selected time duration.

In order to evaluate the normalized time-frequency cross correlationfunction (C_(sr)(t)) for detection and localization, the Wignerdistribution of the reference and reflected signals are to be evaluatedby the equation as follows:

$\begin{matrix}{{W\left( {t,\omega} \right)} = {\frac{1}{2\;\pi}{\int{{s^{*}\left( {t - {\frac{1}{2}\tau}} \right)}{s\left( {t + {\frac{1}{2}\tau}} \right)}{\mathbb{e}}^{- {j\tau\omega}}{\mathbb{d}\tau}}}}} & (5)\end{matrix}$

where W_(s)(t,ω) denotes Wigner Distribution of the input signal. Thenthe Wigner distribution of the input reference signal is obtained asfollows

$\begin{matrix}{{W_{s}\left( {t,\omega} \right)} = {\frac{1}{\pi}{\mathbb{e}}^{{- {\alpha{({t - t_{0}})}}} - {{({\omega - {\beta{({t - t_{0}})}} - \omega_{0}})}^{2}/\alpha}}}} & (6)\end{matrix}$After evaluation of the Wigner distribution of the input reference andreflected signals, the time-frequency cross correlation function fordetection and localization is obtained as follows:

$\begin{matrix}{{C_{sr}(t)} = {\frac{1}{E_{s}{E_{r}(t)}}{\int_{t^{\prime} = {t - T_{s}}}^{t^{\prime} = {t + T_{s}}}{\int{{W_{s}\left( {t,\omega} \right)}{W_{r}\left( {{t^{\prime} - t},\omega} \right)}{\mathbb{d}\omega}\ {\mathbb{d}t^{\prime}}}}}}} & (7) \\{{E_{s} = {\int{\int{{W_{s}\left( {t^{\prime},\omega} \right)}{\mathbb{d}\omega}{\mathbb{d}t}}}}}{{E_{r}(t)} = {\int_{t^{\prime} - t - T_{s}}^{{t\rbrack} = {t + T_{s}}}{{W_{r}\left( {t^{\prime},\omega} \right)}\ {\mathbb{d}\omega}{\mathbb{d}t}}}}} & (8)\end{matrix}$

The time-frequency cross correlation function provided above measurestime-varying similarity of the time-frequency distributions between thereference signal and the reflected signal. Therefore, the existence ofthe reflected signal is to be detected by a quantitative number between0 and 1. A fault in a wire/cable under test can be diagnosed fromexistence of such reflected signal.

However, for a high-accuracy localization of the fault, the distortionof the reflected signals is to be analyzed, which is caused by thewire/cable. The distortion of the reflected signal is the intrinsicsource of localization error in classical time domain reflectometry andfrequency domain reflectometry. However, in time-frequency domainreflectometry, the error caused by the frequency-dependent attenuationcan be compensated by the evaluation of the time offset in associatedwith the frequency offset Consider the propagation of the referencesignal in the wire/cable under test.

As the signal propagates along the media with spatial variable x, thewaveform will be changed by the transfer function of the media H(ω,x).Let u(x,t) be a waveform that is observed at a distance, $×$, for agiven initial condition, u(x,t)=s(t), then, the general solution of theu(x,t) is,

$\begin{matrix}{{u\left( {x,t} \right)} = {\frac{1}{\sqrt{2\pi}}{\int{{S\left( {\omega,x} \right)}{\mathbb{e}}^{{- {j\omega}}\; t}{\mathbb{d}\omega}}}}} & (9)\end{matrix}$

Thus, an input signal in a frequency domain after having progressed by xcan be represented through a multiplication of the initial input signalby transfer function of the medium. Furthermore, since a transferfunction of the medium is determined by α(ω): frequency-dependentattenuation, k(ω): dispersion, the following Formula can be obtained:H(ω,x)=Ce ^(−(α(ω)−jk(ω))x) C: normalization factor   (10)

Therefore, the input reference signal transmitted by distance x throughthe media is obtained as follows:

$\begin{matrix}{{H\left( {x,t} \right)} = {\frac{1}{\sqrt{2\pi}}{\int{{S\left( {\omega,{x = 0}} \right)}{H\left( {\omega,x} \right)}{\mathbb{e}}^{{- {j\omega}}\; t}{\mathbb{d}\omega}}}}} & (11)\end{matrix}$

When the input signal propagates through a wire/cable without thefrequency-dependent attenuation, the transmitted signal maintains ashape identical with that of the initial signal with only a time delay,t_(d) corresponding to the propagation distance in the wire/cable undertest. However, the input reference signal suffers a frequency-dependentattenuation in the transmission through the medium, i.e., wire/cableunder test in this experiment. In particular, attenuation of highfrequencies becomes apparent in wire/cable under tests, which phenomenoncauses shifts of the time center on time axis and the frequency centeron frequency axis of the input signal to new t_(u(x)) ω_(u(x)),respectively, leading to errors in localization of the faults.

Since the input signal is architected to be in a linear section of α(ω)and k(ω), α(ω)≅Aω, k(ω)≅Kω can be assumed. Thus, a time center on a newtime axis, t_(u(x)) of the input signal as transmitted through themedium can be obtained as follows:

$\begin{matrix}{t_{u{(x)}} = {\int{t{{u\left( {x,t} \right)}}^{2}{\mathbb{d}t}}}} & (12) \\{\mspace{40mu}{= {{{Re}\left\lbrack {\int{{S^{*}\left( {\omega,x} \right)}\left( {{- \frac{1}{j}}\frac{\partial}{\partial\omega}{S\left( {\omega,x} \right)}} \right){\mathbb{d}\omega}}} \right\rbrack} = {Kx}}}} & (13)\end{matrix}$

where ν denotes progression speed of the input signal in the medium whenthe frequency is ω_(u(x)). The center frequency, ω_(u(x)) on frequencyaxis can be obtained in the same manner as follows:

$\begin{matrix}{\omega_{u{(x)}} = {\int{\omega{{S(\omega)}}^{2}{\mathbb{d}\omega}}}} & (14) \\{\mspace{50mu}{= {{\omega_{0} - {\frac{\alpha^{2} + \beta^{3}}{\alpha}{Ax}}} = {\omega_{0} - {\delta\omega}}}}} & (15)\end{matrix}$

Therefore, the delay time compensated by β factor and δω of the chirpsignal, which is the input signal of real wave is as follows:

$\begin{matrix}{t_{d} = {{t_{u{(x)}} - t_{s} + \frac{\delta\omega}{\beta}} = {{\Delta\; t} + {\delta\; t}}}} & (16)\end{matrix}$

By summarizing the values obtained above, we can obtain a time-frequencydomain distribution chart as illustrated in FIG. 5. Information on thelocation of faults in a wire/cable under test (d_(f)) as well as on thetotal length of the wire/cable under test (d_(t)) can be obtained fromthe above data as follows:

$\begin{matrix}{{d_{f} = \frac{v \cdot t_{d}}{2}},{d_{t} = {v \cdot t_{d}}}} & (17)\end{matrix}$

FIGS. 6, 7, and 8 show experiment conditions for actual experiments of awire/cable under test in accordance with an implementation of thepresent invention. FIG. 6 shows a schematic construction of experimentfor a wire/cable under test to be tested in accordance with animplementation of the present invention. FIG. 7 illustrates time domain(a) and frequency domain (b) marginals of the time-frequencydistributions of the individual signals in FIG. 9. (Note that theindividual distributions are normalized for illustration. Time centersare shifted to that of the reference signal.) FIG. 8 illustratesphysical characteristics of the wire/cable under test in this experimentin terms of amplitude in (a) and phase in (b).

In the exemplary experiment, an actual wire/cable under test of radioguide (RG)-141 type by advanced design system (ADS) is configured: aninput reference signal as designed in the present invention is appliedto the wire/cable under test, and then, operations of detecting andlocating faults in the wire/cable under test have been performed byprocessing the inputted signal as well as the reflected signal inaccordance with the processing method described above.

Characteristic data of a wire/cable under test in its normal state areeasily obtainable from manufacturer of that wire/cable under test.Therefore, the data can be used for design of an appropriate inputreference signal e.g. with the following parameters:

Time  duration  of  chirp:  30  nsFrequency  bandwidth:  900  MHz  (100  MHz ∼ 1  GHz)${Frequency}\mspace{14mu}{sweep}\text{:}\mspace{14mu}{Linear}\mspace{14mu}{increasing}\mspace{14mu}\left( {\beta = \frac{900\mspace{14mu}{MHz}}{30\mspace{14mu}{ns}}} \right)$

When the input signal described above is transmitted through thewire/cable under test, information on the reflected signal and thetransmitted signal can be acquired from an oscilloscope, at node 1 andnode 2, respectively, in FIG. 9. In Table 1, the experimental resultdata obtained using the time-frequency cross correlation function inFormula (7) are summarized. From the experimental result, localizationof the reflected signal alone is obtainable, and from the time-frequencydomain distribution of each signal, a time center on time axis, t_(s), afrequency center on frequency axis, f_(s), a time duration of the signalT_(s), and a frequency bandwidth, B_(s), of each signal can be obtained.The process of obtaining the values on Table 1 can be summarized asfollows:

-   -   {circle around (1)} The time series of reference and reflected        signals as shown in FIG. 8 can be acquired by the oscilloscope.    -   {circle around (2)} The existence of the reflected signal is        determined by the time-frequency cross correlation function for        the localization in time domain.    -   {circle around (3)} Each signal can be localized through        measuring similarities between the input signal and the        reflected signal using the time-frequency correlation function,        and then classifying them by a threshold value.    -   {circle around (4)} Then, each oft he localized signal is        expressed in a time-frequency domain using Wigner distribution,        and projected to time-frequency axis, to obtain a result as        shown m FIG. 10.    -   {circle around (5)} The values shown in Table 1 obtained from a        result are to be utilized for the time offset evaluation which        is to be converted from the frequency offset. The experimental        result values obtained by the experiments are summarized in        following Table 1:

TABLE 1 Reference Reflected Transmitted Signal Signal Signal Time Center71.94 360.11 361.14 (t_(s), ns) Time Duration 20.17 18.30 21.05 (T_(s),ns) Frequency Center 0.6039 0.5352 0.5778 (f_(s), GHz) FrequencyBandwidth 0.3960 0.3432 0.4245 (B_(s), GHz)

Since the relative dielectric constant of the wire/cable under test isε_(r)=2.1, transmission speed of the input signal in the medium is:

$\begin{matrix}{v = {\frac{c}{\sqrt{ɛ_{r}}} = {\frac{3 \times 10^{8}}{\sqrt{2.1}} = {2.07 \times 10^{8}\left( {m\text{/}\sec} \right)}}}} & (18)\end{matrix}$

From the time center on time axis of the input signal (t_(s)=71.97) andthe time center on time axis of the reflected signal (t_(r)=360.11), adifference of Δt=360.11−71.94=288.17(ns) can be obtained. The positionof a fault can be localized as follows directly from Δt above:

$d = {\frac{{v \cdot \Delta}\; t}{2} = {\frac{2.07 \times {10^{8} \cdot 288.17} \times 10^{- 9}}{2} = {29.8256(m)}}}$

The method of localizing a fault by compensating distortion caused by amedium proceeds as follows:

${\delta\; t\mspace{14mu}{is}\mspace{14mu}\delta\; t} = {\frac{\delta\; f}{\beta}\mspace{14mu}{in}\mspace{14mu}{Formula}\mspace{14mu}{(16).}}$

Since δt represents the difference between frequency center of an inputsignal and that of a reflected signal, δf=0.6039−0.5352=0.0687 (GHz).Since β was set to 3.00×10¹⁶ Hz/sec, when the input signal wasarchitected, we can obtain

${{\delta\; t} = {\frac{\delta\; f}{\beta} = {\frac{0.0687 \times 10^{9}}{3.00 \times 10^{16}} = {2.29{({ns}).\mspace{11mu}\;{Thus}}}}}},{a\mspace{14mu}{result}},{t_{d} = {{{\Delta\; t} + {\delta\; t}} = {{288.17 + 2.29} = {290.46({ns})}}}}$can be obtained from Formula (16).

From Formula (17), we can obtain a localization of the fault as follows:

$d_{f} = {\frac{v \cdot t_{d}}{2} = {\frac{\left( {2.07 \times 10^{8}} \right) \cdot \left( {290.46 \times 10^{- 9}} \right)}{2} = {30.00(m)}}}$

Since information on the reflected signal is also known from theexperiment, information on the total length of the wire/cable under testcan be obtained in the same manner.

Δt, between the input signal and the transmitted signal, can be obtainedfrom Table 1, as δt=361.14−71.94=289.20 (ns). Likewise, δt between theinput signal and the transmitted signal can be obtained from

${\delta\; t} = {\frac{\delta\; f}{\beta}.}$Since the δt between the input signal and the transmitted signal isδf=0.6038−0.5778=0.0261 (GHz), we can obtain:

${\delta\; t} = {\frac{\delta\; f}{\beta} = {\frac{0.0261 \times 10^{9}}{3.00 \times 10^{16}} = {0.87{({ns}).}}}}$

Thus, a result, d_(t)=v·t_(d)=(2.07×10⁸)·(290.07×10⁻⁹)=60 (m) can beobtained, which allows us to localize fault in a wire/cable under testwith an error range of 0.2%.

Although the present invention has been described above with referenceto a specific preferred implementation and wire/cable under test, itshould not be confined by the exemplary application, because one of themain feature of the time-frequency domain reflectometry is the designflexibility of the reference signal depending upon the wire/cable undertest. However, the feasibility of the high-resolution detection andhigh-accuracy localization is valid as long as the reference signal isdesigned in time and frequency domain.

INDUSTRIAL APLICABILITY

As described above, the present invention provides a new time-frequencydomain reflectometry (TFDR) method, wherein an input signal isarchitected to fit to a wire/cable under test considering both time andfrequency and then, the input signal as well as the reflected signalfrom faults in the wire/cable under test are analyzed using atime-frequency analysis method.

Time-frequency domain reflectometry is a new instrumentation andmeasurement technology based on an advanced signal processing, namelytime-frequency analysis. Most contemporary reflectometry instrumentationand measurement devices are based on either the time domain or frequencydomain only for detection and localization of faults, and impedancemeasurement. This limits the performance in accuracy and resolution.However, joint time-frequency domain reflectometry allows one to applyreflectometry in both time domain and frequency domain together so thathigher accuracy and resolution can be achieved. Therefore,time-frequency domain reflectometry can be applied to a variety ofindustries where high precision measurement and testing is requiredcommunications, instrumentation & measurement, material engineering,semiconductors and aerospace & aeronautical etc.

In addition to diagnosis of electric conductors, it can be applied tosystems requiring high level of security such as aircraft and spaceshuttle industries, geographic/resources surveys, material surfacetests, radar/sonar purposes, communication network wirings, opticalcable diagnoses, remote explorations, fluid pipe leakage detections,water gauges, etc., to allow a real-time diagnosis and monitoring ofsuch system, and to enhance stability of the total system, byeffectively assisting automatic maintenance of the system. Moreover, thetime-frequency domain reflectometry can be directly applied tocommercial instrumentation devices for the enhancement of performance,e.g., cable testers and impedance analyzers. Also time-frequency domainreflectometry can provide an improved solution to smart wiring systemsand signal integrity problems where high resolution and accuracy arerequired.

The invention claimed is:
 1. A time-frequency domain reflectometryapparatus for detecting and locating faults in an electric conductorcomprising: a wire/cable to be tested; an arbitrary wave form generatorthat generates a designed input reference signal in time and frequencydomain for said conductor under test; a data acquisition instrument thatstores said reference signal and said reflected signal from saidconductor under test, and transmits stored files to a device controlprogram of a personal computer; a personal computer (PC) configured toperform a main control program of a predetermined time-frequency domainreflectometry, including: a device control program that controls dataacquisition devices, determines time delay, voltage offset, and samplinglevel of a wave form, and architects an input signal, a time-frequencydomain analysis control program that analyzes time-frequency domain ofsaid reference signal and of said wave data reflected from saidwire/cable, and a digital signal processing control program thatreceives said files of said reference signal and said reflected waveinput at said data acquisition instrument through a general purposeinterface bus, and then transmits the files to a digital signalprocessor; and a digital signal processor that computes with a DSPprogram of said time-frequency domain analysis control program, todetect and locate faults in said conductor, by calculatingtime-frequency distribution function of said reflected signal.
 2. Thetime-frequency domain reflectometry apparatus of claim 1, wherein saidinput reference signal generated by said waveform generator is a chirpsignal having a Gaussian envelope with a selected time distribution anda selected frequency domain, of which the frequency changes with time.3. The time-frequency domain reflectometry apparatus of claim 2, whereinsaid data acquisition instrument stores data values of said input signaland said reflected signal as two thermal vectors representing a timevalue and a voltage value, respectively, in a form of files.
 4. Thetime-frequency domain reflectometry apparatus of claim 3, wherein saiddigital signal processor computes time-frequency cross correlationfunction from time-frequency distribution function of input signal inputfrom said PC and time-frequency distribution function of said reflectedwave; and further computes existence and location of faults in saidconductor from said time-frequency cross correlation function.
 5. Thetime-frequency domain reflectometry apparatus of claim 1, wherein saiddata acquisition instrument stores data values of said input signal andsaid reflected signal as two thermal vectors representing a time valueand a voltage value, respectively, in a form of files.
 6. Thetime-frequency domain reflectometry apparatus of claim 5, wherein saiddigital signal processor computes time-frequency cross correlationfunction from time-frequency distribution function of input signal inputfrom said PC and time-frequency distribution function of said reflectedwave; and further computes existence and location of faults in saidconductor from said time-frequency cross correlation function.
 7. Atime-frequency domain reflectometry method for detecting and locatingfaults in an electric conductor, comprising: architecting an inputsignal localized simultaneously in a time domain and a frequency domain;generating said architected input signal; inputting said generated inputsignal into said conductor; receiving a reflected wave reflected fromsaid conductor; transmitting said received reflected wave to a personalcomputer (PC); computing time-frequency distribution functions of saidreflected wave and said input signal by measuring said reflected wave ofsaid input signal; computing a time-frequency cross correlation functionof said time-frequency distribution functions of said reflected wave andsaid input signal; computing a time difference between a time center ofsaid input signal and a time center of said reflected wave from saidtime-frequency cross correlation function; and computing a location ofany fault or a distance by multiplying a progress speed of wave in saidconductor by said time difference.
 8. A time-frequency domainreflectometry method for detecting and locating faults in an electricconductor, comprising: architecting an input signal localizedsimultaneously in a time domain and a frequency domain; generating saidarchitected input signal; inputting said generated input signal intosaid conductor; receiving a reflected wave reflected from saidconductor; transmitting said received reflected wave to a personalcomputer (PC); computing time-frequency distribution functions of saidreflected wave and said input signal by measuring said reflected wave ofsaid input signal; computing a time-frequency cross correlation functionof said time-frequency distribution functions of said reflected wave andsaid input signal; computing a time difference between a time center ofsaid input signal and a time center of said reflected wave from saidtime-frequency cross correlation function; and computing a location ofany fault or a distance by multiplying a progress speed of wave in saidconductor by said time difference; wherein a time duration, a frequencyband width, and a frequency center of said input signal is architectedconsidering attenuation characteristics and expected measuring distanceof said conductor.
 9. A time-frequency domain reflectometry method fordetecting and locating faults in an electric conductor, comprising:architecting an input signal localized simultaneously in a time domainand a frequency domain; generating said architected input signal;inputting said generated input signal into said conductor; receiving areflected wave reflected from said conductor; transmitting said receivedreflected wave to a personal computer (PC); computing time-frequencydistribution functions of said reflected wave and said input signal bymeasuring said reflected wave of said input signal; computing atime-frequency cross correlation function of said time-frequencydistribution functions of said reflected wave and said input signal;computing a time difference between a time center of said input signaland a time center of said reflected wave from said time-frequency crosscorrelation function; and computing a location of any fault or adistance by multiplying a progress speed of wave in said conductor bysaid time difference; wherein said input signal is a chirp signal havinga Gaussian envelope with a selected time distribution and a selectedfrequency domain.
 10. A time-frequency domain reflectometry method fordetecting and locating faults in an electric wire/cable, comprising:architecting an input signal localized simultaneously in a time domainand a frequency domain; generating said architected input signal;inputting said generated input signal into said conductor; receiving areflected wave reflected from said conductor; transmitting said receivedreflected wave to a personal computer (PC); computing time-frequencydistribution functions of said reflected wave and said input signal bymeasuring said reflected wave of said input signal; computing atime-frequency cross correlation function of said time-frequencydistribution functions of said reflected wave and said input signal;computing a time difference between a time center of said input signaland a time center of said reflected wave from said time-frequency crosscorrelation function; localizing time-frequency distribution functionsof said input signal and of said reflected signal from said timefrequency cross correlation function, computing a time offset bycalculating frequency displacement between said input reference signaland said reflected signal, and dividing said frequency displacementbetween said input signal and said reflected signal by time-frequencyincrease rate of said architected input signal, after the frequencymarginal has been obtained from frequency domain of time-frequencydistribution functions of said localized input signal and said reflectedsignal; computing a compensated time difference by adding said timedifference to said time offset; and computing a location of any fault ora distance by multiplying said progress speed in said conductor by saidcompensated time difference.
 11. A time-frequency domain reflectometrymethod for detecting and locating faults in an electric wire/cable,comprising: architecting an input signal localized simultaneously in atime domain and a frequency domain; generating said architected inputsignal; inputting said generated input signal into said conductor;receiving a reflected wave reflected from said conductor; transmittingsaid received reflected wave to a personal computer (PC); computingtime-frequency distribution functions of said reflected wave and saidinput signal by measuring said reflected wave of said input signal;computing a time-frequency cross correlation function of saidtime-frequency distribution functions of said reflected wave and saidinput signal; computing a time difference between a time center of saidinput signal and a time center of said reflected wave from saidtime-frequency cross correlation function; localizing time-frequencydistribution functions of said input signal and of said reflected signalfrom said time frequency cross correlation function, computing a timeoffset by calculating frequency displacement between said inputreference signal and said reflected signal, and dividing said frequencydisplacement between said input signal and said reflected signal bytime-frequency increase rate of said architected input signal, after thefrequency marginal has been obtained from frequency domain oftime-frequency distribution functions of said localized input signal andsaid reflected signal; computing a compensated time difference by addingsaid time difference to said time offset; and computing a location ofany fault or a distance by multiplying said progress speed in saidconductor by said compensated time difference; wherein a time duration,a frequency band width, and a frequency center of said input signal isarchitected considering attenuation characteristics and expectedmeasuring distance of said conductor.
 12. A time-frequency domainreflectometry method for detecting and locating faults in an electricwire/cable, comprising: architecting an input signal localizedsimultaneously in a time domain and a frequency domain; generating saidarchitected input signal; inputting said generated input signal intosaid conductor; receiving a reflected wave reflected from saidconductor; transmitting said received reflected wave to a personalcomputer (PC); computing time-frequency distribution functions of saidreflected wave and said input signal by measuring said reflected wave ofsaid input signal; computing a time-frequency cross correlation functionof said time-frequency distribution functions of said reflected wave andsaid input signal; computing a time difference between a time center ofsaid input signal and a time center of said reflected wave from saidtime-frequency cross correlation function; localizing time-frequencydistribution functions of said input signal and of said reflected signalfrom said time frequency cross correlation function, computing a timeoffset by calculating frequency displacement between said inputreference signal and said reflected signal, and dividing said frequencydisplacement between said input signal and said reflected signal bytime-frequency increase rate of said architected input signal, after thefrequency marginal has been obtained from frequency domain oftime-frequency distribution functions of said localized input signal andsaid reflected signal; computing a compensated time difference by addingsaid time difference to said time offset; and computing a location ofany fault or a distance by multiplying said progress speed in saidconductor by said compensated time difference; wherein said input signalis a chirp signal having a Gaussian envelope with a selected timedistribution and a selected frequency domain.